Most of us tend to use the two terms interchangably, but most contractors would agree that there is a technical difference between the two.
"Remodeling" can be thought of as "reshaping", as in adding a wall, or another bathroom, or even an addition to your home.
"Renovating", on the other hand, typically refers to upgrading or repairing something, like changing a window, flooring tile or a new shower for your basement bathroom.
If your basement is completely unfinished, we would most likely be looking at a remodel. If it is finished - and you are happy with the layout (size of rooms, where the walls are, existing plumbing, etc.), we would refer to it as a renovation.
Either way, the costs for both vary and neither is automatically more or less expensive.